On hub location problems in geographically flexible networks

In this paper, we propose an extension of the uncapacitated hub location problem where potential positions hubs are not fixed in advance. Instead, they allowed to belong a region around initial discrete set nodes. We give general framework which collection, transportation, and distribution costs based on norm-based distances hub-activation setup depend only that opened but also size placed. Two alternative mathematical programming formulations proposed. The first one is compact formulation while second involves family constraints exponential separate efficiently giving rise branch-and-cut algorithm. results extensive computational experience reported showing advantages each approaches.